A farmer has a 200 ft by 40 ft rectangular field that he wants to reduce to 45% of its original size. How wide of a strip should he cut around the edge of his field to do this?

Answer 1

200x40=8000

.45x8000= 4400

(200-2x)(40-2x)=4400

8000-480x +4x^2=4400

2000-120x +x^2 = 1100

x^2 -120x +900 =0

factor, complete the square or use the quadratic formula

x^2 -120x + 60^2 = -900 +60^2

(x-60)^2 =3600-900 = 2700

x-60 = -sqr2700 = -30sqr3

x = 60 - 30(1.732)

x = 60-3(17.32)

x = 60-51.96

= 8.04 feet

he needs to cut a strip of about 8 feet around the area

to reduce it to 45% of its current area

rough check on the answer

round 8.04 to 8

200-2(8) by 40-2(8)

200-16 by 40-16

= 184 times 24

= 4416 = close enough to 4400

given the rounding approximations